Question: ${\sqrt[3]{2560} = \text{?}}$
Solution: $\sqrt[3]{2560}$ is the number that, when multiplied by itself three times, equals $2560$ First break down $2560$ into its prime factorization and look for factors that appear three times. So the prime factorization of $2560$ is $2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5$ Notice that we can rearrange the factors like so: $2560 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 = (2\times 2\times 2) \times (2\times 2\times 2) \times (2\times 2\times 2) \times 5$ So $\sqrt[3]{2560} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{5}$ $\sqrt[3]{2560} = 2\times 2\times 2 \times \sqrt[3]{5}$ $\sqrt[3]{2560} = 8 \sqrt[3]{5}$